Cooling arrangement for electrical transmission system

ABSTRACT

An arrangement for cooling high voltage electric power transmission cables, comprising cooling fluid channels located in the core of the cables, cooling means located at the beginning and end of said channels, and means for circulating cooling fluid in predetermined directions through each of said channels.

United States Patent Rasquin Sept. 2, 1975 1 1 COOLING ARRANGEMENT FOR2.969.415 1/1961 Hartill et al 174/19 ELECTRICAL TRANSMISSION SYSTEM3.105.883 10/1963 Higson, Jr. 174/1 1 R X 3.187.080 6/1965 Ball 1 1.174/11 R [75] Inventor: Werner Rasquin, Cologne. Germany 339101 12 1966Kafka 174/15 C 3.485930 12/1969 Priaroggia .t 174/15 C [73] Assgnw FelteGumeaume Kabelwerke 3,800,062 3/1974 Kataoka 174/15 0 AG, Cologne.Germany [22] Filed. Man 22, 1974 FOREIGN PATENTS OR APPLICATIONS1,573,685 7/1969 France 174/l5 C [2]} Appl- 454,237 1,124.08] 8/1968United Kingdom 174 15 c [30] Foreign Application Priority Data PrimaryExaminer-Arthur T. Grimley May 29. 1973 Germany N 2327316 Attorney,Agent, or Firm-Michael S. Striker Aug. 9, 1973 Germany.... 2340328 Sept15. 1973 Germany... 2340507 [57] ABSTRACT 2 U.S. l ..174l5C; 17411R;17414 R; [5 1 C l/74/27 An arrangement for cooling high voltageelectric [5!] Int Cl 2 018 7/34 power transmission cables, comprisingcooling fluid [58] Field 14 R 27 channels located in the core of thecables, cooling H means located at the beginning and end of said chan-[56] References Cited nels, and means for circulating cooling fluid inpredetermined directions through each of said channels. UNITED STATESPATENTS 873,216 12/1907 Davis 174/l5 C 13 Claims, 4 Drawing FiguresPATENTEDSEP zms sum 1 BF 4 PATENTEM 975 sum 2 BF 4 FIG. 2

PATENTEU SEP 2 I975 sum 3 BF 4 FIG. 3

COOLING ARRANGEMENT FOR ELECTRICAL TRANSMISSION SYSTEM BACKGROUND OF THEINVENTION The present invention relates to high voltage electricaltransmission systems, particularly to three phase alternating currentsystems with associated cooling means.

It is generally known to provide circulating fluid cooling devices, suchas oil or water ducts, in the fabrication of high voltage transmissionsystems. Such systems, however, only include one cooling station orheat-exchanging device. After cooling. the fluids enter the system andflow in the same direction. Following circulation and heating by thecable, the fluids are generally returned to the cooling unit in externalreturn flow tubes, which are separate from the transmission cables.

The construction of return flow pipes may be made as separate pipes ortubes, or with three possibly conical isolated electrical conductorsdistributed in a known manner in the return flow pipes (see, forexample, West German published Pat. application No. 1,067,099). In suchan arrangement, should one con ductor or return flow pipe fail, then theentire cable system would become inoperative.

SUMMARY OF THE INVENTION It is an object of the invention to provide acooling arrangement for high voltage electric power transmission cablesutilizing a plurality of cooling fluid channels and at least two coolingunits.

Another object of the invention is to provide a novel and improved meansfor maintaining the system in operation should one of the conductors, orone of the cooling channels, fail.

The invention is embodied in an arrangement of four parallel cables,with a cooling fluid, such as oil or water, flowing in a cooling channelin the center of each cable. At the beginning and end of the cables is acooling station, with cooling means, connected to said cooling channelsso as to receive and cool the cooling fluid therein. The cooling fluidis then recirculated in the system in predetermined specified channelsand directions.

Three of the four cables normally carry electric cur rent, such as in athree phase alternating current sys tem, and the fourth cable serves asa reserve. Should the conductor in one cable or one of the coolingchannels fail, it would be possible to immediately switch over to thereserve cable, and thereby maintain continuous operation of the system.

It is particularly advantageous in such an arrangement to have thecooling fluid flowing in one direction in two of the cables, and flowingin the opposite direction in the other two of the cables. Such anarrangement of continuous recirculation of the cooling fluid is moreeconomical than utilizing separate flow lines to return and recirculatethe fluid. The fourth cable serves the purpose of providing return flowof the cooling fluid, and also serves as a back-up conductor in case ofmalfunction of another cable.

Another feature of the invention is to obtain the maximum technicaladvantage at the least cost. One method of achieving this goal is toutilize intermediate pumping means along the channel and cable, inaddition to the pumping stations at the beginning and end of the cable.Activating the intermediate pumps for the cooling fluid will increasethe throughput of the cooling channels. (i.e., increase the quantity offluid flowing through the channel), and thereby increase the rate ofheat dissipation in the cable. In this manner, one can have a highermaximum permissible power in the cable system than without theintermediate pumps.

Increasing the maximum permissible system power also increases the costof the system, due on the one hand to both the manufacture and assemblyof the intermediate pumps themselves, and a loss due to highinstallation costs on the other hand, bringing about higher overallcost, as well as the costs from construc tion of the cooling station.These higher costs however are associated with a higher output of thetransmission system, more advantageous system length, and increasedlifetime. Thus, when these costs are compared in the long run with theadvantages of long term operation, it would appear to be an economicalchoice in spite of higher construction costs.

A particular embodiment of the invention envisions that the distancebetween cooling stations is more than 10 kilometers, the inner diameterof the cooling fluid channel is from 40 to mm.

The number n of intermediate pumps to be located in the cable systembetween cooling stations may be calculated from the equation where:

K Total cost of the cable system before the installation of intermediatepumps;

K,. Capital costs for the cooling stations before the installation ofintermediate pumps;

K ,v Cost of the power loss before the installation of intermediatepumps.

From the above analysis it follows that operation is most economical ifsmall diameter fluid channels are used with relatively long distancesbetween cooling stations, and wherein the cost of the cooling stations(K together with the cost of power loss (K is less than half of thetotal cost (K,,,,,,,).

The novel features which are considered as characteristic for theinvention are set forth in particular in the appended claims. Theinvention itself, however, both as to its construction and its method ofoperation, together with additional objects and advantages thereof willbe best understood from the following description of specificembodiments when read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a cross-sectional view ofthe cable system arrangement relative to the surface of the earth;

FIG. 2 is a cross-sectional view of a single cable, showing the variouscomponent elements;

FIG. 3 is a diagram of the cable cooling and flow system arrangement;and

FIG. 4 is a graph relating pressure variables and temperature variablesin the system to electrical power transmitted.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a cross-sectionalview of an electrical cable system for power transmission of highintensity. such as over 2 million voltamperes. The figure shows thecable system 1 located beneath the surface of the earth there are fourseparate parallel cables in the system, three normally carrying current(such as in a threephase or three-wire system), and the fourth servingas a back-up or reserve cable. The axes of the four cables are situatedat the corners of a square, one diagonal of which is parallel to thesurface of the earth 5 and has a length 2a, as shown. The reserve cableis the one furthest from the surface of the earth, since it would beused only rarely, it would be subject to the least deterioration overtime.

The figure also shows the spacing a, of the cables 2 from the center ofthe square (not shown), and a schematic cross-section of each cable,with conductor 4, provided with a central channel 3 for cooling fluid.

FIG. 2 illustrates the cross-section of a cable 2 in more detail. In thecenter of the cable a cylindrical tube 6 forming a channel 3 for passageof the cooling fluid, and a concentric conductor 4 of copper or aluminumpiping or wire braid. The tube 6 can be constructed of either metal orplastic.

Outside of the conductor 4 is a smooth conductive lining member 7; andfinally an insulator 8, composed of plastic or oil treated paper.Outside of the insulator 8 is an electrical shield 9, composed of acopper band, for example. This central portion 3, 6, 4, 7, 8, 9 restsinside of an enclosure defining an open space 23 between the centralportion and the enclosure.

The enclosure of the cable is composed of a corrugated tube 10,preferably of aluminum, surrounded by a covering layer 11 of plasticmaterial, and finally another outer sheathing 12 of plastic or othersynthetic material.

FIG. 3 is a diagram of the cooling system arrangement. The diagram showsthe four cables 2, which, in one particular embodiment, haveintermediate pumps 21 uniformly distributed over the length of thecable. The length of the cable may be more than kilometers.

Also shown are fluid monitoring means 20, to measure various parameterssuch as temperature and pressure of the fluid at least at one point ofeach cable, electrical insulating means 13; and three-phase electricgrid wires R,S,I, connected to the electrical conductor 4 of the cablethrough switches 14.

Following another electrical insulating means 15, the fluid channel tube6 extends from the cable and is grounded at 16. The channel preferablyhas a diameter of between 40 and 70 mm.

In normal operation of the system, the cooling fluid circulates in thechannel in the direction shown by the arrows 17, due to the action ofthe circulating pumps 18. The fluid is pumped through two cables,through a first cooling means 5, then back through the other two cables,then through a second cooling means 5, and once again through the twooriginal cables. Valves l9 permit adjustment or cutoff of circulation inany of the channels.

The fluid monitoring devices are able to sense key parameters liketemperature and pressure of the fluid in the channels. In the event ofdisturbance or malfunction of a particular cable and channel, theseparameters would change, thereby alerting the operator of the system.The operator then may immediately switch the grid wire connections bychanging switches 14 to another combination of cables. Furthermore, theoperator may selectively close certain valves 19, to shut off thecooling fluid flow from the channel experiencing a malfunction.

In normal operation, the cooling fluid flow would be in one direction intwo of the cables, and in the opposite direction in the other twocables. In the case of malfunction or disorder in one cable, the coolingfluid would be shut off in that one cable; the fluid would then flow inone direction in two cables, and in the opposite direction in theremaining cable. This circulation distribution makes it possible tomaintain the power level in the transmission system, although thecooling fluid throughput in the cooling channel system, with one channelinoperative, is necessarily lower.

Although it is desirable to avoid lowering the fluid throughput, theeffect is not so great as to require a drastic reduction in power. Thetwo cables in which the water is flowing in the same direction willmerely experience a higher operating temperature; and the fluid flowingin the remaining will experience a rise in operating pressure, comparedwith the operating parameters under normal system operation. Repairs tothe defective cable are not expected to take too much time, and theeffect of higher-than-normal operating temperatures on certain cablesfor a relatively short period of time is not expected to shorten thelife expectancy of such cables significantly.

One consequence of the high electric current able to be carried by thetransmission system is the production of a strong magnetic field in theregion of the conductors. In conventional cable systems, the magneticinduction with neighboring cables will set up eddy currents, creatingadditional heating of the cables.

Another feature of the invention is the'particular arrangment of thefour cables. In the particular embodiment seen in FIG. 1 the axes of thecables are located at the corners of a square; one diagonal of thesquare is parallel to the surface of the earth. Thus, the three cablescarrying current lie on the vertices of an isosceles triangle, and thesingle magnetic field associated with a single cable effectivelyneutralizes the other magnetic fields, at any given time. Furthermore,the cable not carrying current does not sense any significant magneticfield. The region of the transmission system has only a small, stable,net magnetic field, which is independent of which of the three cablesare energized.

The three cables lying closest to the surface of the earth arepreferably the ones used to carry current. In this way, should one ofthe cables require repair, they are relatively close to the surface, andcan therefore, be more easily repaired or replaced.

FIG. 4 is a graph illustrating various relationships be tween keyparameters of the system.

S transmission system power during undisturbed operation.

S transmission system power during disturbed operation.

AT temperature increase in the channel when fluid is flowing in a firstdirection during undisturbed operation.

AT =temperature increase in the channel when fluid is flowing in a firstdirection during disturbed operation.

AP,, pressure drop along the channel in a second opposite direction offlow during undisturbed operation.

AP pressure drop along the channel in a second opposite direction offlow during disturbed operation.

The term undisturbed operation is to be understood as the normaloperation of the system with fluid flowing in two channels in onedirection, and two channels in the other direction. Disturbed operationis to be understood as the operation when one of the fluid channels isblocked, so that fluid flows in one channel in one direction, and in twochannels in the opposite direction.

Examining the curves in FIG. 4, one can see that the combination ofoperating parameters expressed above correspond to the 5/5 1 curve, i.e.the electrical power transmission during disturbed operation is the sameas during undisturbed operation.

lf the operating range of the pressure and temperature parameters of thesystem do not allow particular levels (96C and 84 bar), then theelectrical power transmission during disturbed operation will besomewhat less than during undisturbed operation, corresponding to /8,,curves below the S/S 1 curve in FIG. 4. On such curves the pressuredifference and/or the temperature difference during disturbed operationwould be lower.

The form of the curves themselves are derived as follows: The electricalpower capable of being transmitted through the cable is proportional tothe fluid throughput. Thus 5,, -AT,, V AP and the curves are given by Anexample using specific operating parameters should clarify therelationships expressed in FIG. 4.

Suppose, in normal operation. the temperature T, of the fluid enteringthe channel is 30C, and the temperature T of the fluid leaving thechannel is 85C. The corresponding pressure P, of the fluid entering thechannel is 31 bar, and the pressure P of the fluid leaving the channelis 1 bar. Therefore A7), 8530C 55C; and AP 3ll bar 30 bar.

Further supposing that during disturbed operation T 30C, T 96C, so thatAT= 66C. The corresponding pressure difference is AP 83 bar.

The ratios of the l. differences A7}, and AI, and pressure differencesAP,, and AP, during undisturbed and disturbed operation are:

In this case, if the temperature difference along the two cables whichconduct cooling medium in one direction in the disturbance caseincreases by relative to the operating temperature difference in theundisturbed state, then the pressure difference along the individualcables with oppositely directed current direction must be more thandoubled.

While the invention has been illustrated and described as embodied in acooling arrangement for an electrical transmission system, it is notintended to be limited to the details shown, since various modificationsand structural changes may be made without departing in any way from thespirit of the present invention.

Without further analysis, the foregoing will so fully reveal the gist ofthe present invention that others can, by applying current knowledgereadily adapt it for various applications without omitting featuresthat, from the standpoint of prior art, fairly constitutes essentialcharacteristics of the generic or specific aspects of this inventionand, therefore, such adaptations should and are intended to becomprehended within the meaning and range of equivalence of thefollowing claims.

What is claimed as new and desired to be protected by Letters Patent isset forth in the appended:

l. A three-phase power-transmission cable system, comprising, incombination, a first set of three phase lines at a first location, and asecond set of three phase lines at a second location remote from saidfirst location; three cables and a fourth cable constituting a reservecable, said three cables and said fourth cable adjoining each other andeach spanning the distance from said first location to said secondlocation and having respective first ends at said first location andrespective second ends at said second location, each cable including anelectrical conductor and an internal channel for the flow of a coolingmedium in heat-exchanging relationship with the respective electricalconductor along the length of the respective cable from one to the otherof said first and second locations; electrical switching means operativeduring normal operation for electrically connecting said conductors ofsaid three cables at the first ends thereof to respective ones of thethree phase lines of said first set and at the second ends thereof torespective ones of the three phase lines of said second set whileleaving at least one end of the conductor of said reserve cableelectrically unconnected to said phase lines, and operative in the eventof failure of one of said three cables for connecting the phase linesassociated with the conductor of the failed cable to the respective endsof the conductor of said reserve cable; and cooling means operativeduring normal operation for establishing a flow of cooling mediumthrough the internal channels of said three cables and also said reservecable, whereby in the event of failure of one of said three cables andestablishment of electrical connections between the phase linesassociated with the failed cable and the respective ends of theconductor of said reserve cable the heat generated within said reservecable will be immediately removed by the cooling medium already flowingtherethrough.

2. A system as defined in claim 1, wherein said three cables and saidreserve cable are each a one-conductor cable.

3. A system as defined in claim 1, wherein said cooling means includes afirst cooling station at said first location and a second coolingstation at said second location, and connecting means connecting saidfirst cooling station to the first ends of said three cables and of saidreserve cable and connecting said second cooling station to the secondends of said three cables and of said reserve cable to establish atleast one closed flow circuit for the flow of cooling medium through theinternal channels of said three cables and of said reserve cable andthrough said first and second cooling stations.

4. A system as defined in claim 1, wherein said cooling means includes afirst cooling station at said first location and a second coolingstation at said second location, each of said cooling stations havingrespective inlet means for receipt of higher-temperature cooling mediumand respective outlet means for the discharge of cooled and thereforelower-temperature cooling medium, and connecting means connecting theinternal channels of two of said cables at the first ends thereof to theinlet means of the first cooling station and at the second ends thereofto the outlet means of the second cooling station, and connecting theinternal channels of the remaining two of said cables at the first endsthereof to the outlet means of the first cooling station and at thesecond ends thereof to the inlet means of the second cooling station,and fluid impelling means for effecting flow of cooling fluid from theoutlet means of said first cooling station to the inlet means of saidsecond cooling station through the channels of two cables in onedirection and for effecting flow of cooling fluid from the outlet meansof the second cooling station to the inlet means of the first coolingstation through the channels of the two remaining cables in the oppositedirection.

5. A system as defined in claim 4, wherein said cooling means includesmeans operative in the event of failure of one of said three cables andestablishment of electrical connections between the phase linesassociated with the failed cable and the respective ends of theconductor of said reserve cable for blocking flow of fluid through theinternal channel of the failed cable so that cooling fluid flows in onedirection through two of the three operating cables and in the oppositedirection through the remaining one of the three operating cables.

6. A system as defined in claim 5, wherein the dimensions of saidinternal channels, of said connecting means, and of the flow passages insaid cooling stations and in said fluid impelling means, the coolingcapacity of said cooling stations and the throughput of said fluidimpelling means are such that when the flow of fluid through the failedcable is blocked the temperature of the two cables through which coolingmedium flows in the same direction and also the pressure of the coolingmedium in the remaining one of the three operating cables are higherthan during normal operation but such as to leave the transmission ofelectrical power through the cable system the same as during normaloperation.

7. A system as defined in claim 1, wherein each of said three cables andsaid reserve cable is a oneconductor cable the conductor of which ishollow, with the hollow interior of the conductor defining therespective internal channel.

8. A system as defined in claim 1, wherein said cooling means includesfour intermediate pumps, each connected in the flow path of the internalcooling channel of a respective one of said cables intermediate thefirst and second ends thereof.

9. A system as defined in claim I, wherein said cooling means includesfour groups of intermediate pumps, the number of pumps being the same ineach of said groups, and the pumps of each group being connected in theflow path of the internal cooling channel of a respective one of saidcables intermediate the first and second ends of the respective cableand uniformly spaced along the length of the respective cable.

10. A system as defined in claim 1, wherein the distance between saidfirst and second locations is greater than 10 kilometers, and whereinthe flow diameter of each of said internal channels is between 40 andmillimeters, and wherein the number of intermediate pumps in each ofsaid four groups is equal to n, where n mml)/( cs loss) 1 1 wherein:

K the total cost of the cable system before installation of theintermediate pumps,

K capital cost of the cooling means before the installation of theintermediate pumps,

K cost of the power loss in the cables before the installation of theintermediate pumps.

11. A system as defined in claim 3, wherein the flow of cooling mediumin said system from said first location to said second location and alsofrom said second location back to said first location is exclusivelythrough the internal channels of said cables.

12. In an electrical transmission system, particularly for thetransmission of high voltage electrical power, a combination comprisinga plurality of cables each spanning the distance between a firstlocation and a second location remote from the first location, eachcable comprising an electrical conductor and an internal channel for theflow of a cooling medium; cooling means comprising at least discretefirst and second units, said first unit being at said first location andcommunicating with the first ends of said internal channels and saidsecond unit being at said second location and communicating with thesecond ends of said internal channels; and means for circulating coolingmedium in said channels, such that the flow in one of said channels iscounter to the flow in another of said channels, wherein the number ofsaid cables is four, and said system is a three-phase alternatingcurrent system, wherein a combination of three of said cables carrieselectric current while the fourth cable serves as a reserve, whereinsaid cables are located beneath the surface of the earth, wherein eachof said cables is located at one of the corners of a quare, and whereina diagonal of said square in parallel to said surface of the earth.

13. A combination as defined in claim 12, wherein said fourth cable isthat which lies furthest from said surface of the earth.

1. A three-phase power-transmission cable system, comprising, incombination, a first set of three phase lines at a first location, and asecond set of three phase lines at a second location remote from saidfirst location; three cables and a fourth cable constituting a reservecable, said three cables and said fourth cable adjoining each other andeach spanning the distance from said first location to said secondlocation and having respective first ends at said first location andrespective second ends at said second location, each cable including anelectrical conductor and an internal channel for the flow of a coolingmedium in heat-exchanging relationship with the respective electricalconductor along the length of the respective cable from one to the otherof said first and second locations; electrical switching means operativeduring normal operation for electrically connecting said conductors ofsaid three cables at the first ends thereof to respective ones of thethree phase lines of said first set and at the second ends thereof torespective ones of the three phase lines of said second set whileleaving at least one end of the conductor of said reserve cableelectrically unconnected to said phase lines, and operative in the eventof failure of one of said three cables for connecting the phase linesassociated with the conductor of the failed cable to the respective endsof the conductor of said reserve cable; and cooling means operativeduring normal operation for establishing a flow of cooling mediumthrough the internal channels of said three cables and also said reservecable, whereby in the event of failure of one of said three cables andestablishment of electrical connections between the phase linesassociated with the failed cable and the respective ends of theconductor of said reserve cable the heat generated within said reservecable will be immediately removed by the cooling medium already flowingtherethrough.
 2. A system as defined in claim 1, wherein said threecables and said reserve cable are each a one-conductor cable.
 3. Asystem as defined in claim 1, wherein said cooling means includes afirst cooling station at said first location and a second coolingstation at said second location, and connecting means connecting saidfirst cooling station to the first ends of said three cables and of saidreserve cable and connecting said second cooling station to the secondends of said three cables and of said reserve cable to establish atleast one closed flow circuit for the flow of cooling medium through theinternal channels of said three cables and of said reserve cable andthrough said first and second cooling stations.
 4. A system as definedin claim 1, wherein said cooling means includes a first cooling stationat said first location and a second cooling station at said secondlocation, each of said cooling stations having respective inlet meansfor receipt of higher-temperature cooling medium and respective outletmeans for the discharge of cooled and therefore lower-temperaturecooling medium, and connecting means connecting the internal channels oftwo of said cables at the first ends thereof to the inlet means of thefirst cooling station and at the second ends thereof to the outlet meansof the second cooling station, and connecting the internal channels ofthe remaining two of said cables at the first ends thereof to the outletmeans of the first cooling station and at the second ends thereof to theinlet means of the second cooling station, and fluid impelling means foreffecting flow of cooling fluid from the outlet means of said firstcooling station to the inlet means of said second cooling stationthrough the channels of two cables in one direction and for effectingflow of cooling fluid from the outlet means of the second coolingstation to the inlet means of the first cooling station through thechannels of the two remaining cables in the opposite direction.
 5. Asystem as defined in claim 4, wherein said cooling means includes meansoperative in the event of failure of one of said three cables andestablishment of electrical connections between the phase linesassociated with the failed cable and the respective ends of theconductor of said reserve cable for blocking flow of fluid through theinternal channel of the failed cable so that cooling fluid flows in onedirection through two of the three operating cables and in the oppositedirection through the remaining one of the three operating cables.
 6. Asystem as defined in claim 5, wherein the dimensions of said internalchannels, of said connecting means, and of the flow passages in saidcooling stations and in said fluid impelling means, the cooling capacityof said cooling stations and the throughput of said fluid impellingmeans are such that when the flow of fluid through the failed cable isblocked the temperature of the two cables through which cooling mediumflows in the same direction and also the pressure of the cooling mediumin the remaining one of the three operating cables are higher thanduring normal operation but such as to leave the transmission ofelectrical power through the cable system the same as during normaloperation.
 7. A system as defined in claim 1, wherein each of said threecables and said reserve cable is a one-conductor cable the conductor ofwhich is hollow, with The hollow interior of the conductor defining therespective internal channel.
 8. A system as defined in claim 1, whereinsaid cooling means includes four intermediate pumps, each connected inthe flow path of the internal cooling channel of a respective one ofsaid cables intermediate the first and second ends thereof.
 9. A systemas defined in claim 1, wherein said cooling means includes four groupsof intermediate pumps, the number of pumps being the same in each ofsaid groups, and the pumps of each group being connected in the flowpath of the internal cooling channel of a respective one of said cablesintermediate the first and second ends of the respective cable anduniformly spaced along the length of the respective cable.
 10. A systemas defined in claim 1, wherein the distance between said first andsecond locations is greater than 10 kilometers, and wherein the flowdiameter of each of said internal channels is between 40 and 70millimeters, and wherein the number of intermediate pumps in each ofsaid four groups is equal to n, where n ((Ktotal)/(Kcs + Kloss) - 1)2 -1 wherein: Ktotal the total cost of the cable system before installationof the intermediate pumps, Kcs capital cost of the cooling means beforethe installation of the intermediate pumps, Kloss cost of the power lossin the cables before the installation of the intermediate pumps.
 11. Asystem as defined in claim 3, wherein the flow of cooling medium in saidsystem from said first location to said second location and also fromsaid second location back to said first location is exclusively throughthe internal channels of said cables.
 12. In an electrical transmissionsystem, particularly for the transmission of high voltage electricalpower, a combination comprising a plurality of cables each spanning thedistance between a first location and a second location remote from thefirst location, each cable comprising an electrical conductor and aninternal channel for the flow of a cooling medium; cooling meanscomprising at least discrete first and second units, said first unitbeing at said first location and communicating with the first ends ofsaid internal channels and said second unit being at said secondlocation and communicating with the second ends of said internalchannels; and means for circulating cooling medium in said channels,such that the flow in one of said channels is counter to the flow inanother of said channels, wherein the number of said cables is four, andsaid system is a three-phase alternating current system, wherein acombination of three of said cables carries electric current while thefourth cable serves as a reserve, wherein said cables are locatedbeneath the surface of the earth, wherein each of said cables is locatedat one of the corners of a quare, and wherein a diagonal of said squarein parallel to said surface of the earth.
 13. A combination as definedin claim 12, wherein said fourth cable is that which lies furthest fromsaid surface of the earth.